Seemingly overnight, my iPhone 5 went from working normally to requiring very firm presses to register the home button. I've tried the single water drop trick posted on Youtube (put a single drop of water on the home button and rub it around while holding the button pressed), and I've tried the "recalibration" trick (go to a factory installed app, hold the power button until "swipe to turn off" appears, then hold the home button until it goes away). I've tried using an isopropyl alcohol wipe on the home button the same way I would with the drop of water.
Overall, the sensitivity improved, but there are still many "lost clicks" on the home button if I'm not specifically thinking about clicking it hard. It is out of warranty and the nearest Apple store is 90 minutes away.